Tuning the Schottky barrier height in single- and bi-layer graphene-inserted MoS2/metal contacts

First-principle calculations based on density functional theory are employed to investigate the impact of graphene insertion on the electronic properties and Schottky barrier of MoS2/metals (Mg, Al, In, Cu, Ag, Au, Pd, Ti, and Sc) without deteriorating the intrinsic properties of the MoS2 layer. The results reveal that the charge transfer mainly occurs at the interface between the graphene and metal layers, with smaller transfer at the interface between bi-layer garphene or between graphene and MoS2. And the tunneling barrier exists at the interface between graphene and MoS2, which hinders electron injection from graphene to MoS2. Importantly, the Schottky barrier height (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Phi_{{\text{SB,N}}}$$\end{document}ΦSB,N) decreases upon graphene insertion into MoS2/metal contacts. Specifically, for single-layer graphene, the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Phi_{{\text{SB,N}}}$$\end{document}ΦSB,N of MoS2 contacted with Mg, In, Sc, and Ti are − 0.116 eV, − 0.116 eV, − 0.014 eV, and − 0.116 eV, respectively. Furthermore, with bilayer graphene, when by inserting bi-layer graphene, the negative n-type Schottky barrier of − 0.086 eV, − 0.114 eV, − 0.059 eV, − 0.008 eV, and − 0.0636 eV are observed for MoS2 contacted with the respective metals, respectively. These findings provide a practical guidance for developing and designing high-performance transition metal dichalcogenide nanoelectronic devices.

Two-dimensional (2D) transition metal dichalcogenides (TMDs) have attracted considerable attention as potential channel materials for next-generation nanoelectronic devices due to their atomic thickness, high carrier mobility, low concentration of surface dangling bonds, and suitable band gap [1][2][3] .Previous studies on 2D MoS 2 transistors have demonstrated excellent field-effect mobility with high on-off ratio at room temperature [4][5][6] .However, due to the Fermi level pinning, the contact resistance of MoS 2 /metal contact is up to 5 kΩ•μm-1 MΩ•μm, which is more than 30 times larger than that of the Si/metal 7,8 .This high contact resistance poses a significant barrier to realizing the low power application potential of MoS 2 -based devices.
The origin of high contact resistance for MoS 2 /metal remains unclear, even though several factors have been proposed, including the wide contact tunnel barrier, the high Schottky barrier ( SB ), and high intrinsic resistance of semiconductor channel [9][10][11] .In principle, the transport properties of 2D materials devices are often limited by the contact tunnel barrier and Schottky barrier rather than the intrinsic resistance.Efforts have been made to mitigate Schottky barrier by employing low work function metals.For instance, Das et al. 4 achieved enhanced effective mobilities by using scandium contacts on exfoliated MoS 2 flakes covered by a 15 nm Al 2 O 3 film.However, to date, the reported lowest contact resistance using scandium electrode is still far from satisfactory.Novel doping strategies for TMDs have also been explored to reduce the Schottky barrier [12][13][14][15] .However, the reliable doping technology with precise control over doping concentration and doping profile for 2D transistors 16 .Recent experiments have demonstrated significant Schottky barrier reduction when ultrathin tunnel layer is inserted between MoS 2 and metal electrode [17][18][19][20][21][22] .For example, through a dry transfer technique and a metal-catalyzed graphene treatment process, Leong et al. 23 fabricated nickel-etched-graphene electrodes on MoS 2 that yield contact resistance as low as 200 Ω•μm.Du et al. 24 claimed that MoS 2 /graphene/Ti Schottky barrier provides electron injection efficiency up to 130 times higher in the subthreshold regime when compared with MoS 2 /Ti, which resulted in V DS polarity dependence of device parameters such as threshold voltage (V TH ) and subthreshold www.nature.com/scientificreports/swing (SS).Chanana et al. 25 proposed that unlike MoS 2 /metal contacts, the projected dispersion of MoS 2 remains preserved in MoS 2 /graphene/metal contacts with shift in the bands on the energy axis.A proper choice of metal may exhibit ohmic nature in a graphene-inserted MoS 2 /metal contact.Moreover, Qiu et al. 26 demonstrated that the contacts of the multi-layered MoS 2 /graphene have tunable negative barriers in the range of 300 to − 46 meV as a function of gate voltage.Thus, 2D materials insertion shows great potential to effectively adjust the contact properties of MoS 2 /metal contacts.
Graphene has been identified as an effective approach to adjust the work function of the metal 27 .it interacts strongly with the metals, such as Co, Ni, Pd and Ti, which involves hybridization between graphene p z states and metal d states and reduces considerably the work function of the metal 28 .Moreover, the substantial potential drop (8.881 eV) between MoS 2 and graphene could promote the charge transfer from graphene to MoS 2 layer.In this work, we investigate the electronic properties and Schottky barrier of MoS 2 /metals (Mg, Al, In, Cu, Ag, Au, Pd, Sc, and Ti) by inserting single-and bi-layer graphene based on density functional theory (DFT).Our study reveals that the tunneling barrier existed at the interface between graphene and MoS 2 , which hinders electron injection from graphene to MoS 2 .We achieved the decrease of SB,N upon graphene insertion in MoS 2 /metal contacts.The results are systematically discussed, and provide valuable insights for design of high-performance device.

Computational details
First-principle calculations based on DFT were carried out by using the Vienna ab initio simulation package (VASP) 29,30 .The projector augmented wave (PAW) method 31 was used to describe the electron-ion core interaction, which is more accurate than the ultra-soft pseudo-potentials.The Perdew-Burke-Ernzerhof (PBE) 32 formulation of the generalized gradient approximation (GGA) was chosen to describe the exchange-correlation interaction.Since the semi-local functional, such as, GGA fail to describe weakly interacting systems, the van der Waals interaction in the Grimme approach was adopted to describe the weak interlayer interaction 33 .The cutoff energy for the plane-waves was chosen to be 450 eV.The Brillouin-zone integration was performed by using an 11 × 11 × 1 k-mesh according to the Monkhorst-Pack scheme and Gaussian smearing broadening of 0.05 eV was adopted.To avoid artificial interactions between the periodic images of the structures, a vacuum region of at least 15 Å was used.A conjugate-gradient algorithm was employed to relax the ions to the ground states with an energy convergence of 1.0 × 10 -5 eV and a force convergence of 0.02 eV/Å on each ion, respectively.Visualizations of supercell and structure were done with the software VESTA 34 .

Results and discussions
The optimized structures of single-layer graphene and MoS 2 are shown in Fig. 1a,b, with the lattice constants of 2.460 Å and 3.160 Å, respectively, which is consistent with previous experimental and theoretical results. 35,36In the optimized configurations, the bond lengths of C-C and Mo-S are 1.406 and 2.413 Å, respectively.
For the in-plane lattice mismatch within δ 1 and δ 2 ( ≤ 5% ), the supercells of the contacts are usually larger with a broken symmetry.Based on this approach, the CSL of MoS 2 , graphene, and metal are modeled, and the parameters are listed in Table 1 1, the lattice constant mismatches are all less than 5%.Similarly, the MoS 2 /metal contacts by inserting bi-layer graphene are also constructed and as shown in Fig. 1d.
Figures 2 and 3 display the charge density difference of MoS 2 /metal by inserting single-and bi-layer graphene, respectively.The charge density difference is calculated as: (1)     www.nature.com/scientificreports/ in which ρ contact , ρ MS , ρ i , and ρ M are the charge densities of the contact system, the isolated MoS 2 , inserting layer (single-or bi-layer graphene), and metal, respectively.As shown in Figs. 2 and 3, the charge transfer mainly occurs at the interface between the graphene and metal layers, with smaller transfer at the interface between bi-layer garphene or between graphene and MoS 2 .Specifically, the charge transfer oscillation occurs near the interface between graphene and Sc/Ti, indicating strong interaction and the formation of interfacial dipole layers.Furthermore, the Bader charge analysis has also been conducted for those interfaces.The Bader charge distribution of MoS  and 0.042 e at the interface between the graphene and MoS 2 , respectively, indicating weak interactions between them.For MoS 2 / metal contact by inserting bi-layer graphene, the interactions between metal and graphene, as well as between graphene and MoS 2 are similar to that of the MoS 2 /metal contact by inserting singly-layer graphene.
To investigate the effects of the inserting singly-layer and bi-layer graphene on the electron tunnel of MoS 2 / metal contact, the average effective potential in the x-y plane normal to the interface and the tunneling barrier V are calculated, as shown in Figs. 4 and 5, respectively.The height V defined as the potential energy above E F between graphene and metal, bi-layer graphene, as well as garphene and MoS 2 , and its width ω B is defined as the full width at half maximum of V .The barrier height reflects the lowest barrier that electrons at E F need to overcome upon injection between neighboring layers.With singly-layer graphene, no tunneling barrier exists at the graphene/metal interface.However, there is noticeable tunneling barrier at exists at the graphene/MoS 2 interface with the values of V are 0.568 eV, 1.889 eV, 1.456 eV, 0.309 eV, 1.061 eV, 0.111 eV and 0.313.The cor- responding values of ω B are 0.422 Å, 0.826 Å, 0.654 Å, 0.292 Å, 0.562 Å, 0.153 Å, and 0.252 Å for Mg, Al, In, Ag, Au, Pd, and Sc, respectively (excluding Cu and Ti).For inserting bi-layer graphene, the tunneling barrier only exists at the interface between graphene and Al, and the values of V and ω B are 0.420 eV and 0.164 Å, respec- tively; At the interface between bi-layer graphene for Al, In, Au, and Sc, the values of V are 1.320 eV, 0.620 eV, 0.181 eV, and 0.296 eV, as well as the values of ω B are 0.281 Å, 0.233 Å, 0.246 Å, and 0.192 Å, respectively; At the interface between graphene and MoS 2 for Al, Mg, In, Cu, Ag, Au, Pd, Sc, and Ti, the values of V are 1.070 eV, 2.604 eV, 1.990 eV, 0.566 eV, 0.586 eV, 1.270 eV, 0.466 eV, 1.590 eV and 0.360 eV, as well as the values of ω B are where m is the effective mass of a free electron and is the Planck's constant.The T B values at the interface between graphene and MoS 2 in the MoS 2 /metal contact by inserting singly-layer graphene are estimated to be 88%, 62.2%, 69.7%, 93.1%, 77.4%, 97.8%, and 94% for MoS 2 contacted with Mg, Al, In, Ag, Au, Pd, and Sc, respectively.For MoS 2 /metal contact with bi-layer graphene insertion, the T B values at the interface between graphene and Al are estimated to be 96.5%;The T B values at the interface between bi-layer graphene are estimated to be 89.7%,94.0%, 96.5% and 96.5% for Al, In, Au, and Sc, respectively; The T B values at the interface between graphene and MoS 2 are estimated to be 87.4%,80.5%, 89.2%, 95.6%, 92.4%, 88.2%, 93.4%, 85.1%, and 96.4% for Mg, Al, In, Cu, Ag, Au, Pd, Sc, and Ti, respectively.Therefore, inserting graphene is not determinant to the tunneling transmission in MoS 2 /metal contacts.
As shown in Figs. 6 and 7, the partial density of states (PDOS) of graphene and MoS 2 sublayers in MoS 2 / metal contacts by inserting single-and bi-layer graphene has been studied, respectively.While graphene does not introduce an additional contact barrier, it induces significant change of electronic structure on itself.For the MoS 2 /metal contact by inserting singly-layer graphene, the Dirac cone gets shifted and below Fermi level for Mg, Al, In, Cu, and Ag, but exhibits opposite trend for Au.Moreover, the Dirac nature is completely lost when MoS 2 contacted with Pd, Sc, and Ti.The same phenomenon occurs for graphene which is adjacent to metal layer in the MoS 2 /metal contact by inserting bi-layer graphene, but the Dirac cone is not perturbed for graphene which is adjacent to MoS 2 layer.Compared to the free monolayer MoS 2 , although the semiconductor future is maintained, the energy band alignment and band gap of the MoS 2 in MoS 2 /metal by inserting single-and bi-layer graphene have changed.For inserting singly-layer graphene, the conduction band of MoS 2 across Fermi level when contacted with Mg, In, Sc, and Ti, while the Fermi level lies in the band gap and closes to the conduction band minimum of MoS 2 when contacted with Al, Cu, Ag, Au, and Pd, indicating an n-type semiconductor.The values of band gap are 1.567 eV, 1.526 eV, 1.540 eV, 1.562 eV, 1.562 eV, 1.553 eV, 1.536 eV, 1.482 eV, and 1.540 eV (4)

Conclusions
In this study, the effects of inserting single-and bi-layer graphene on the electronic properties and Schottky barrier of MoS 2 /metals (Mg, Al, In, Cu, Ag, Au, Pd, Ti, and Sc) are studies by using first-principle calculations based on density functional theory.Our findings indicate significant charge value at the interface between graphene and metals, leading to the absence of tunneling barrier appears in the MoS 2 /metal contact by inserting singly-layer graphene.By contrast, the tunneling barrier exists at the interface between graphene and MoS 2 , suggests hindering in electron injection.Additionally, the SB,N is reduced when graphene is inserted in MoS 2 / metal contacts.When MoS 2 contacted with Mg, In, Sc, and Ti by inserting single-layer graphene, the SB,N of − 0.116 eV, − 0.116 eV, − 0.014 eV, and − 0.116 eV, respectively.On the other hand, bi-layer graphene insertion leads to the negative n-type Schottky barriers of − 0.086 eV, − 0.114 eV, − 0.059 eV, − 0.008 eV, and − 0.0636 eV for MoS 2 contacted with Mg, In, Pd, Sc, and Ti, respectively, indicating transition to the Ohmic contact.Our findings offer valuable insights for the design and optimization of nanoelectronic devices, utilizing MoS 2 /graphene/metal interfaces, highlighting the potential for enhanced device performance through graphene insertion.

Table 2 .
Calculated interfacial properties of MoS 2 /metals by inserting single-layer and bi-layer graphene.d M-G , d G-G , and d G-MS , as marked in Fig. 1c,d, are the average vertical separation between the metal and graphene, between bi-layer graphene, and between graphene and MoS 2 , respectively.W M and W M/G (W M/2G ) are the work functions of the free-standing metal surfaces and adsorbed single-layer (bi-layer) graphene, respectively.a Reference 28 .b Reference 37 .c Reference 38 .

Figure 2 .
Figure 2. Plane-average charge density difference along the z-direction of MoS 2 /metals by inserting single-layer graphene.
2 /metal contact by inserting single-layer graphene exhibits the average charge values of 0.035 e, 0.052 e and 0.049 e at the interface of the graphene/Mg, Al, and In, respectively, showing weak interactions.Medium interaction are observed at the interface of graphene/Cu, Ag, and Au with the average charge values of 0.069 e, 0.070 e and 0.073 e, respectively.The average charge values of 0.101 e, 0.125 e and 0.208 e at the interface between the graphene and Pd, Sc, and Ti, respectively, indicating strong interactions between them.However, the average charge values of 0.032 e, 0.042 e, 0.034 e, 0.038 e, 0.042 e, 0.042 e, 0.046 e, 0.039 e,

Figure 3 .
Figure 3. Plane-average charge density difference along the z-direction of MoS 2 /metals by inserting bi-layer graphene.

Figure 4 .Figure 5 .
Figure 4. Plane-average electronic potential along the z-direction of MoS 2 /metals by inserting single-layer graphene.

Figure 6 .
Figure 6.Partial density of states (PDOS) of graphene and MoS 2 layers in MoS 2 /metals by inserting single-layer graphene.